The Taliban have captured the strategic city of Ghazni, 95 miles (150km) south of Kabul, as they continued to tighten their grip on the Afghan capital and the country’s president replaced his army chief.

The insurgent group had control of the entire city on Thursday morning and had broken into a prison and released about 400 inmates, a senior local official confirmed to the Guardian.

The assault reportedly began at around midnight, leading to heavy street-to-street clashes with security forces. By 8am the Taliban were in control of most of the city. “The local police commander and governor were desperate and had no other option and joined the Taliban,” the official said. “People are hiding in their homes, nobody is out.”

The loss of Ghazni, the 10th provincial capital to fall in less than a week, is a major blow for the Afghan government, because the city is located on the highway connecting Kabul to southern Afghanistan. It comes two days after the Taliban captured the key city of Pul-e-Khumri, 140 miles north of the capital, giving the insurgents control of a strategic road junction linking Kabul to the north and west.

Fighting also raged on Thursday in Lashkar Gah, one of Afghanistan’s largest cities in the Taliban heartland of Helmand province, where government forces are surrounded after the militants’ weeklong blitz.

The government hopes to hold on to Lashkar Gah, but a suicide car bombing on Wednesday was the latest attack to target the regional police headquarters.

By Thursday, the Taliban had taken the building. Some police officers surrendered to the militants and others retreated to the nearby governor’s office, which was still held by government forces, said Nasima Niazi, a lawmaker from Helmand.

Niazi said she believed the Taliban attack killed and wounded members of the security forces members, but she had no casualty figures.

Another suicide car bombing targeted the provincial prison, but the government still held it, she said.

The Taliban have freed hundreds of their members over the last week, bolstering their ranks while seizing US-supplied weapons and vehicles.

Niazi criticised ongoing airstrikes targeting the area, saying civilians were likely to have been killed or wounded. “The Taliban used civilian houses to protect themselves, and the government, without paying any attention to civilians, carried out airstrikes,” she said.

Afghan security forces and the government have not responded to repeated requests for comment over the days of fighting. President Ashraf Ghani is, however, trying to rally a counteroffensive relying on his country’s special forces, the militias of warlords and American airpower ahead of the US and Nato withdrawal at the end of the month.

Ghani appointed Gen Hibatullah Alizia as his new army chief, the Afghan defence ministry said late on Wednesday, replacing Gen Wali Mohammad Ahmadzai, who had only been in post since June.

The Afghan defence ministry also tweeted on Wednesday that Sami Sadat, a young general hailed for his defence of Lashkar Gah, had been promoted to lead the country’s special forces.

Sadat, 36, commands the 20,000-strong 215th Corps in Lashkar, and told Agence France-Presse on Wednesday that he was confident he could defend the city. “I know this is our country, that the Taliban are failing, that they will fail sooner or later,” he said by phone.

Kabul itself has not been directly threatened in the Taliban’s advance, but the stunning speed of the offensive raises questions about how long the Afghan government can maintain control of the slivers of the country it has left.

It may eventually be forced to pull back to defend the capital and just a few other cities. Thousands of people displaced by the fighting have fled to Kabul and now live in open fields and parks.

The fighting around Lashkar Gah has raged for weeks. Afghan air power is limited and in disarray, and the US air force is believed to be carrying out strikes to support Afghan forces. Aviation tracking data suggested B-52 bombers, F-15 fighter jets, drones and other aircraft were involved in the fighting overnight across the country, according to the Australia-based security firm, Cavell Group.

It was unclear how many casualties the US bombing campaign has caused. The US air force central command, based in Qatar, did not immediately respond to a request for comment on Thursday.

The success of the Taliban offensive also calls into question whether they would ever rejoin long-stalled peace talks in Qatar intended to move Afghanistan toward an inclusive interim administration as the west hoped. The insurgents could instead come to power by force – or the country could splinter into factional fighting as it did after the Soviet withdrawal in 1989.

The latest US military intelligence assessment is that Kabul could come under insurgent pressure within 30 days and that if current trends hold, the Taliban could gain full control of the country within a couple of months.